Method for controlling a fuel cell system having a hydrogen fuel injector/ejector

ABSTRACT

A method for controlling a fuel cell system having a hydrogen fuel injector/ejector and a control system, includes determining a hydrogen fuel consumption rate associated with a selected power level at steady state, determining a modeled hydrogen fuel flow rate associated with the selected power level and the injector/ejector, determining a modeled effective flow area associated with the injector/ejector, determining a true effective flow area of the injector/ejector, and using the effective flow area to calculate or adjust a command signal, an estimation or an estimation error of at least one of a hydrogen fuel flow rate, an anode leak rate and an anode exhaust valve flow rate.

INTRODUCTION

This disclosure relates generally to methods for operating andcontrolling a fuel cell system having a hydrogen fuel injector/ejector.

Fuel cell systems operate by converting hydrogen and oxygen into waterand electricity, utilizing an anode and a cathode which are disposed inelectrochemical communication with each other.

An injector, an ejector or a combined injector/ejector is used tointroduce hydrogen gas into the anode at a metered rate in response to acontrol signal sent to the injector/ejector. However, the effectiveorifice area of the injector/ejector may vary over time and from part topart, which may cause undesirable variations in the performance of thefuel cell system.

SUMMARY

According to one embodiment, a method is provided for controlling a fuelcell system having a hydrogen fuel injector/ejector and a controlsystem. In this embodiment, the method includes: determining a hydrogenfuel consumption rate {dot over (n)}_(TrsntConsum) associated with aselected power level at steady state; obtaining a modeled hydrogen fuelflow rate {dot over (n)}_(injSp_Model) associated with the selectedpower level and the injector/ejector; estimating a true effective flowarea A_(Eff_True) of the injector/ejector, whereinA_(Eff_True)=A_(Eff_Model)·({dot over (n)}_(TrsntConsum)/{dot over(n)}_(injSp_Model)) and A_(Eff_Model) is a modeled effective flow areaassociated with the injector/ejector; and using the effective flow areaA_(Eff_True) to calculate or adjust a command signal, an estimation oran estimation error of at least one of a hydrogen fuel flow rate, ananode leak rate and an anode exhaust valve flow rate.

At the selected power level at steady state, an anode pressure may bemaintained at a constant pressure. The modeled hydrogen fuel flow rate{dot over (n)}_(injSp_Model) may be obtained from a first look-up tableassociated with the control system or may be calculated by the controlsystem. Similarly, the modeled effective flow area A_(Eff_Model) may beobtained from a second look-up table associated with the control systemor may be calculated by the control system. The method may furtherinclude operating the fuel cell system at the selected power level andat steady state, in order to determine the hydrogen fuel consumptionrate {dot over (n)}_(TrsntConsum) associated with the selected powerlevel at steady state.

The fuel cell system may include a proportional-integral-adaptive (PIA)controller operatively associated with the injector/ejector.Additionally, the true effective flow area A_(Eff_True) may be estimatedusing A_(Eff_True)=A_(geo)·Coeff_(DC)·(1+a^(new)), wherea^(new)=F_(x)·{dot over (n)}_(TrsntConsum)/({dot over(n)}_(TrsntConsum)+{dot over (n)}_(Leak_Model))−1 and F_(x)≈1+I_(A)·∫edt+p_(A)·e+a^(old). In these equations, A_(geo) is an orifice area ofthe injector/ejector that is determinable at a calibration event,Coeff_(DC) is an orifice discharge coefficient of the injector/ejectorthat is determinable at the calibration event, a^(new) is an updatedadaption term, F_(x) is an injector/ejector flow adjustment factoroutput from the PIA controller, {dot over (n)}_(Leak_Model) is an anodeleak rate calculated by {dot over (n)}_(Leak_Model)={dot over(n)}_(injSp_Model)−{dot over (n)}_(TrsntConsum), I_(A) is an integralgain of the PIA controller, p_(A) is a proportional gain of the PIAcontroller, e is an error of the PIA controller modeled by {dot over(n)}_(injSp_Model)−{dot over (n)}_(TrsntConsum), ∫e dt is a timeintegral of the error e, and a^(old) is a previous adaption term storedin a non-volatile memory associated with the control system.

The method may further include storing the updated adaption term a^(new)in the non-volatile memory, or it may include replacing the previousadaption term a^(old) stored in the non-volatile memory with the updatedadaption term a^(new). Additionally, the anode leak rate {dot over(n)}_(Leak_Model) may be an averaged anode leak rate stored in thenon-volatile memory.

According to another embodiment, a method of operating a fuel cellsystem having a hydrogen fuel injector/ejector, an anode, aproportional-integral-adaptive (PIA) controller operatively associatedwith the injector/ejector, a control system and a non-volatile memoryassociated with the control system includes: (i) operating the fuel cellsystem at a power level for a predetermined time; (ii) determining ahydrogen fuel consumption rate {dot over (n)}_(TrsntConsum) associatedwith the power level; (iii) obtaining a modeled hydrogen fuel flow rate{dot over (n)}_(injSp_Model) associated with the selected power leveland the injector/ejector; (iv) finding an anode leak rate {dot over(n)}_(Leak_Model) of the anode, where {dot over (n)}_(Leak_Model)={dotover (n)}_(injSp_Model)−{dot over (n)}_(TrsntConsum); and (v)calculating an adaption term a^(new), where a^(new)=(1+I_(A)·∫edt+p_(A)·e+a^(old))·{dot over (n)}_(TrsntConsum)/({dot over(n)}_(TrsntConsum)+{dot over (n)}_(Leak_Model))−1, in which I_(A) is anintegral gain of the PIA controller, p_(A) is a proportional gain of thePIA controller, e is an error of the PIA controller modeled by {dot over(n)}_(injSp_Model)−{dot over (n)}_(TrsntConsum), ∫e dt is a timeintegral of the error e, and a^(old) is a previously calculated orprovided adaption term stored in the non-volatile memory.

The method may further include storing the calculated adaption terma^(new) in the non-volatile memory. Alternatively, the method mayinclude comparing the calculated adaption term a^(new) with thepreviously calculated or provided adaption term a^(old), and replacingthe previously calculated or provided adaption term a^(old) in thenon-volatile memory with the calculated adaption term a^(new) if thedifference between the adaption terms a^(old) and a^(new) is greaterthan a predetermined value. The method may further include storing theanode leak rate {dot over (n)}_(Leak_Model) in the non-volatile memory.

The embodiment above may further include repeating the operating,determining, obtaining, finding and calculating steps for a plurality oftimes for different power levels from the initial power level. In eachrepeat of the calculating step, the respective calculated adaption terma^(new) may be stored in the non-volatile memory as either (i) areplacement for a previously calculated adaption term or (ii) an averageand/or accumulation of some or all of the previous adaption terms. Themethod may also include estimating a true effective flow areaA_(Eff_True) of the injector/ejector, using one ofA_(Eff_True)=A_(Eff_Model)·({dot over (n)}_(TrsntConsum)/{dot over(n)}_(injSp_Model)) and A_(Eff_True)=A_(geo)·Coeff_(DC)·(1+a^(new)), inwhich A_(Eff_Model) is a modeled effective flow area associated with theinjector/ejector, A_(geo) is an orifice area of the injector/ejector andCoeff_(DC) is an orifice discharge coefficient of the injector/ejector,and using the effective flow area A_(Eff_True) to calculate or adjust acommand signal, an estimation or an estimation error of at least one ofa hydrogen fuel flow rate, an anode leak rate and the anode exhaustvalve flow rate. At the selected power level at steady state, an anodepressure may be maintained at a constant pressure. Each of the modeledhydrogen fuel flow rate {dot over (n)}_(injSp_Model) and the modeledeffective flow area A_(Eff_Model) may be obtained from a look-up tableassociated with the control system or may be calculated by the controlsystem.

According to yet another embodiment, a method of operating a fuel cellsystem having a hydrogen fuel injector/ejector, an anode, aproportional-integral-adaptive (PIA) controller operatively associatedwith the injector/ejector, a control system and a non-volatile memoryassociated with the control system, includes: (i) operating the fuelcell system at a power level for a predetermined time; (ii) determininga hydrogen fuel consumption rate {dot over (n)}_(TrsntConsum) associatedwith the power level; (iii) obtaining a modeled hydrogen fuel flow rate{dot over (n)}_(injSp_Model) associated with the selected power leveland the injector/ejector; (iv) finding an anode leak rate {dot over(n)}_(Leak_Model) of the anode, where {dot over (n)}_(Leak_Model)={dotover (n)}_(injSp_Model)−{dot over (n)}_(TrsntConsum); (v) calculating anadaption term a^(new), where a^(new)=(1+I_(A)·∫edt+p_(A)·e+a^(old))·{dot over (n)}_(TrsntConsum)/({dot over(n)}_(TrsntConsum)+{dot over (n)}_(Leak_Model))−1, in which I_(A) is anintegral gain of the PIA controller, p_(A) is a proportional gain of thePIA controller, e is an error of the PIA controller modeled by {dot over(n)}_(injSp_Model)−{dot over (n)}_(TrsntConsum), ∫e dt is a timeintegral of the error e, and a^(old) is a previously calculated orprovided adaption term stored in the non-volatile memory; (vi) comparingthe calculated adaption term a^(new) with the previously calculated orprovided adaption term a^(old); (vii) replacing the previouslycalculated or provided adaption term a^(old) in the non-volatile memorywith the calculated adaption term a^(new) if the difference between theadaption terms a^(old) and a^(new) is greater than a predeterminedvalue; (viii) repeating the operating, determining, obtaining, finding,calculating, comparing and replacing steps (i.e., (i) through (vii)) fora plurality of times for different power levels from the initial powerlevel; (ix) estimating a true effective flow area A_(Eff_True) of theinjector/ejector, using one of A_(Eff_True)=A_(Eff_Model)·({dot over(n)}_(TrsntConsum)/{dot over (n)}_(injSp_Model)) andA_(Eff_True)=A_(geo)·Coeff_(DC)·(1+a^(new)) in which A_(Eff_Model) is amodeled effective flow area associated with the injector/ejector,A_(geo) is an orifice area of the injector/ejector and Coeff_(DC) is anorifice discharge coefficient of the injector/ejector; and (x) using theeffective flow area A_(Eff_True) to calculate or adjust a commandsignal, an estimation or an estimation error of at least one of ahydrogen fuel flow rate, an anode leak rate and the anode exhaust valveflow rate.

The above features and advantages, and other features and advantages, ofthe present teachings are readily apparent from the following detaileddescription of some of the best modes and other embodiments for carryingout the present teachings, as defined in the appended claims, when takenin connection with the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic view of a fuel cell system.

FIG. 2 is a schematic view of an anode for a fuel cell system.

FIG. 3 is a flowchart for a method of controlling or operating a fuelcell system.

DETAILED DESCRIPTION

Referring now to the drawings, wherein like numerals indicate like partsin the several views, a fuel cell system 20 and a method 100 foroperating or controlling the fuel cell system 20 are shown and describedherein.

The present disclosure describes a methodology for estimating aneffective flow area of the injector/ejector 40, referred to herein as atrue effective flow area A_(Eff_True), which may be used to overcomeinjector/ejector flow rate estimation errors and inaccuracies. Themethodology provides fast adaption to fix injector/ejector flow rateerror by addressing the flow area variation which can occur due topart-to-part size variations (e.g., due to manufacturing tolerances) andsize/flow variations which may arise over the life of a giveninjector/ejector 40. Effectively addressing this variation as describedherein provides a “correction factor” which can be used to correct oradjust a command signal, an estimation or an estimation error of thehydrogen fuel flow rate 70, the anode leak rate 72 and/or the anodeexhaust valve flow rate 74, all of which are affected byinjector/ejector flow rate, and thus are also affected by variations inthe effective flow area of the injector/ejector 40 over time.

FIGS. 1 and 2 show schematic views of a fuel cell system 20 and an anode24 for a fuel cell system 20, respectively. The fuel cell system 20 maybe operated at one or more power levels, and includes a fuel cell stack22 which has an anode 24 and a cathode 26. Hydrogen gas is fed from ahydrogen source 28 to the anode 24 via an anode input line 30, andoxygen or air is fed from a compressor 42 or other oxygen/air source tothe cathode 26 via a cathode input line 44. The anode input line 30includes a temperature sensor 32 or a modeled temperature, an injectioninlet pressure sensor 34, an injector/ejector 40, an anode pressuresensor 54, and a proportional-integral (PI) controller 58 operativelyassociated with the anode pressure sensor 54. As shown in FIG. 2 , theinjector/ejector 40 may include an injector or injector portion 36 andan ejector or ejector portion 38. As used herein, an “injector/ejector”40 may be an injector 36, or an ejector 38, or both an injector 36 andan ejector 38. In cases where the injector/ejector 40 includes both aninjector 36 and an ejector 38, these two components may be combined intoa single unified structure, or they may be disposed as two separatestructures that are disposed in series with each other. Theinjector/ejector 40 may also include or be operatively associated with aproportional-integral-adaptive (PIA) controller 56, which may be used tocontrol and/or monitor the flow of hydrogen gas through theinjector/ejector 40.

An anode exhaust line 46 extends from an exit of the anode 24, and acathode exhaust line 48 extends from an exit of the cathode 26. Theanode exhaust line 46 may carry unused hydrogen gas away from the anode24, and the cathode exhaust line 48 may carry unused oxygen/air awayfrom the cathode 26. In either or both of the exhaust lines 46, 48,water and other liquids or gases may be carried away from the fuel cellstack 22. An anode exhaust valve 50 may be disposed in the anode exhaustline 46, with the portion of the anode exhaust line 46 that isdownstream of the anode exhaust valve 50 being joined with the cathodeexhaust line 48 and having an anode exhaust valve flow rate 74.

A recirculation line 52 runs from a first end, which is connected with aportion of the anode exhaust line 46 upstream of the anode exhaust valve50, to a second end, which is connected with the injector/ejector 40. Inthis arrangement, some or all of the unused hydrogen gas which passesinto the anode exhaust line 46 from the anode 24 may be directed backinto the anode 24 via the recirculation line 52.

The fuel cell system 20 also includes a control system 60, which mayinclude various control hardware 62 and control software 64, includingnon-volatile memory 66 and one or more look-up tables 68, 69. Thecontrol system 60 may be connected with various sensors, actuators andother devices within the fuel cell system 20, such as the temperaturesensor 32, the pressure sensors 34, 54, the anode exhaust valve 50, thePIA controller 56, the PI controller 58, the compressor/oxygen source 42and the injector/ejector 40.

As shown in FIG. 2 , a flow of hydrogen gas is passed from theinjector/ejector 40 and into the anode 24 at a hydrogen fuel flow rate70, which can be modeled by the control system 60 (e.g., within thecontrol software 64) as a modeled hydrogen fuel flow rate {dot over(n)}_(injSp_Model). Most of the hydrogen gas gets electrochemicallyreacted with oxygen in the fuel cell stack 22 (i.e., consumed) toproduce electricity and water. This majority of the hydrogen gas thatgets consumed and converted into electricity is represented by {dot over(n)}_(TrsntConsum). However, some small portion of the hydrogen gas mayleak out of the anode 24 (e.g., through seals, gaskets, fittings, etc.);this small portion is represented by {dot over (n)}_(Leak_Model), havingan anode leak rate 72. Using a mass-balance approach on the gas inputsand outputs of the anode 24 provides the following mass-balanceequation:

{dot over (n)} _(Leak_Model) ={dot over (n)} _(injSp_Model) −{dot over(n)} _(TrsntConsum)  (Eqn. 1)

The injector/ejector 40 may be operated in range or duty cycle from 0%(with the injector/ejector 40 fully closed and no hydrogen gas flowingtherethrough) to 100% (with the injector/ejector 40 fully open). At anygiven injector/ejector duty cycle (DC), the following equation may beused:

DC=({dot over (n)} _(injSp_True) /{dot over (n)} _(injMax_True))=({dotover (n)} _(injSp_Model) /{dot over (n)} _(injMax_Model))  (Eqn. 2)

where {dot over (n)}_(injSp_True) is an actual hydrogen fuel flow ratefor the given duty cycle, {dot over (n)}_(injMax_True) is an actualmaximum hydrogen fuel flow rate for a 100%/fully open duty cycle, {dotover (n)}_(injSp_Model) is a modeled hydrogen fuel flow rate for thegiven duty cycle as modeled in the control software 64, and {dot over(n)}_(injMax_Model) is a modeled maximum hydrogen fuel flow rate for a100%/fully open duty cycle as modeled in the control software 64. Thisequation (i.e., Eqn. 2) can be rearranged to provide the following:

({dot over (n)} _(injSp_True) /{dot over (n)} _(injSp_Model))=({dot over(n)} _(injMax_True) /{dot over (n)} _(injMax_Model))  (Eqn. 3)

Looking at the right-hand side of Eqn. 3, where both quantities areexpressions of a 100%/fully open duty cycle, along with the fact thatinjector/ejector flow rate is proportional to the injector/ejectororifice effective flow area and considering temperature and gas species(both are hydrogen) are the same, it may be determined that:

({dot over (n)} _(injMax_True) /{dot over (n)} _(injMax_Model))=(A_(Eff_True) /A _(Eff_Model))  (Eqn. 4)

where A_(Eff_True) is the actual injector/ejector orifice effective flowarea and A_(Eff_Model) is the modeled injector/ejector orifice effectiveflow area as modeled in the control software 64. Then, combining Eqns. 3and 4 yields:

({dot over (n)} _(injSp_True) /{dot over (n)} _(injSp_Model))=({dot over(n)} _(injMax_True) /{dot over (n)} _(injMax_Model))=(A _(Eff_True) /A_(Eff_Model))   (Eqn. 5)

or more simply:

({dot over (n)} _(injSp_True) /{dot over (n)} _(injSp_Model))=(A_(Eff_True) /A _(Eff_Model))  (Eqn. 6)

When the fuel cell system 20 is running at steady state, the actualanode gas leakage within a well-designed system should be negligible orvery close to zero and all of the hydrogen gas entering the anode 24 canbe assumed to be converted to electricity, yielding:

{dot over (n)} _(injSp_True) ={dot over (n)} _(TrsntConsum)  (Eqn. 7)

Substituting Eqn. 7 into Eqn. 6 for {dot over (n)}_(injSp_True) yields:

({dot over (n)} _(TrsntConsum) /{dot over (n)} _(injSp_Model))=(A_(Eff_True) /A _(Eff_Model))  (Eqn. 8)

which can be rearranged as:

A _(Eff_True) =A _(Eff_Model)·({dot over (n)} _(TrsntConsum) /{dot over(n)} _(injSp_Model))  (Eqn. 9)

Thus, the actual injector/ejector orifice effective flow areaA_(Eff_True) for the injector/ejector 40 can be found from (i) themodeled injector/ejector orifice effective flow area as modeled in thecontrol software 64 (i.e., A_(Eff_Model)), (ii) the rate that hydrogengas that gets consumed and converted into electricity (i.e., {dot over(n)}_(TrsntConsum)), and (iii) the modeled hydrogen fuel flow rate forthe given duty cycle as modeled in the control software 64 (i.e., {dotover (n)}_(injSp_Model)).

One approach for modeling the injector/ejector effective flow area(i.e., A_(Eff_Model)) in the control software 64 is by using thefollowing expression:

A _(Eff_Model) =A _(geo)·Coeff_(DC) ·F _(x)  (Eqn. 10)

where A_(geo) is an orifice area of the injector/ejector 40 that isdeterminable at a calibration event, Coeff_(DC) is an orifice dischargecoefficient of the injector/ejector 40 that is determinable at thecalibration event, and F_(x) is an injector/ejector flow adjustmentfactor output by or derivable from the PIA controller 56. (Theaforementioned calibration event may occur at the end of productionbefore the fuel cell system 20 is put into production, and/or at somelater point after the injector/ejector 40 has been serviced orreplaced.) The flow adjustment factor F_(x) may be approximated as:

F _(x)≈1+I _(A) ·∫e dt+p _(A) ·e+a ^(old)  (Eqn. 11)

where, I_(A) is an integral gain of the PIA controller 56, p_(A) is aproportional gain of the PIA controller 56, e is an error of the PIAcontroller 56 modeled by {dot over (n)}_(injSp_Model)−{dot over(n)}_(TrsntConsum), ∫e dt is a time integral of the error e, and a^(old)is a previous adaption term stored in non-volatile memory 66. (Forexample, the a^(old) term may be an initial value that is stored in alook-up table 68, 69. Optionally, multiple values for a^(old) may bestored in one or more look-up tables 68, 69, where each value isassociated with a respective power level of the fuel cell system 20.)

However, Eqn. 11 is known to be an approach that is relatively “slow” atarriving at a satisfactory solution, so an improved alternative approachwould be to utilize a relatively “faster” flow adjustment factor oradaption term. For example, the 14 ({dot over (n)}_(TrsntConsum)/{dotover (n)}_(injSp_Model)) portion from Eqn. 9 may be adjoined to Eqn. 10to produce:

A _(Eff_True) =A _(geo)·Coeff_(DC) ·F _(x)·({dot over (n)}_(TrsntConsum) /{dot over (n)} _(injSp_Model))  (Eqn. 12)

where F_(x)·({dot over (n)}_(TrsntConsum)/{dot over (n)}_(injSp_Model))may be considered as a candidate for a newer and “faster” flowadjustment factor.In turn, this newer and “faster” flow adjustment factor may be expressedas the term (1+a^(new)), where a^(new) is an updated adaption term, thusyielding:

F _(x)·({dot over (n)} _(TrsntConsum) /{dot over (n)}_(injSp_Model))=(1+a ^(new))  (Eqn. 13)

and

A _(Eff_True) =A _(geo)·Coeff_(DC)·(1+a ^(new))  (Eqn. 14)

Rearranging Eqn. 13 so as to isolate the updated adaption term a^(new)yields:

a ^(new) =F _(x)·({dot over (n)} _(TrsntConsum) /{dot over (n)}_(injSp_Model))−1  (Eqn. 15)

This new or updated adaption term a^(new) may be stored in non-volatilememory 66 so as to replace the previous adaption term a^(old).Additionally, when further calculations are made for a^(new), these maybe stored to replace previous calculations of the adaption term.

In the control system 60 (e.g., in the control software 64), the modeledhydrogen fuel flow rate set point {dot over (n)}_(injSp_Model) may becalculated in association with the anode pressure proportional-integral(PI) controller 58, expressed as:

{dot over (n)} _(injSp_Model) ={dot over (n)} _(TrsntConsum) +I _(p) ·∫edt+p _(p) ·e  (Eqn. 16)

where I_(p) is an integral gain of the anode pressure PI controller 58,e is an error of the anode pressure PI controller 58 between pressuresetpoint and feedback, ∫e dt is a time integral of the error e, andp_(p) is a proportional gain of the anode pressure PI controller 58.Substituting Eqn. 16 into Eqn. 15 yields:

a ^(new) =F _(x) ·{dot over (n)} _(TrsntConsum)/({dot over (n)}_(TrsntConsum) I _(p) ·∫e dt+p _(p) ·e)−1  (Eqn. 17)

As noted above in Eqn. 1 (and repeated below), the modeled anode leakrate {dot over (n)}_(Leak_Model) is calculated as the difference betweenthe modeled hydrogen fuel flow rate {dot over (n)}_(injSp_Model) and thehydrogen gas consumption rate {dot over (n)}_(TrsntConsum):

{dot over (n)} _(Leak_Model) ={dot over (n)} _(injSp_Model) −{dot over(n)} _(TrsntConsum)  (Eqn. 1)

Substituting the {dot over (n)}_(injSp_Model) expression from Eqn. 16into Eqn. 1 then yields:

{dot over (n)} _(Leak_Model)=({dot over (n)} _(TrsntConsum) +I _(p) ·∫edt+p _(p) ·e)−{dot over (n)} _(TrsntConsum) =I _(p) ·∫e dt+p _(p) ·e  (Eqn. 18)

Then, substituting Eqn. 18 into Eqn. 17 yields:

a ^(new) =F _(x)·({dot over (n)} _(TrsntConsum)/({dot over (n)}_(TrsntConsum) +{dot over (n)} _(Leak_Model)))−1  (Eqn. 19)

With regard to Eqn. 19, it may be noted that the modeled anode leak rate{dot over (n)}_(Leak_Model) may be averaged and stored in non-volatilememory 66 for use in valve flow estimation and to improve calculationreliability which might otherwise be affected by local variations. Also,the hydrogen fuel consumption rate {dot over (n)}_(TrsntConsum) may bedetermined by observing the power consumption of the fuel cell system20, and the injector/ejector flow adjustment factor F_(x) may bedetermined from the PIA controller 56. Thus, all of the terms on theright-hand side of Eqn. 19 should be readily available or determinableso that the adaption factor a^(new) may be found. Once a^(new) isdetermined, the injector/ejector orifice effective flow areaA_(Eff_True) may be corrected/updated, such as by utilizing Eqn. 14.Additionally, the corrected/updated effective flow area A_(Eff_True) mayalso be used to calculate or adjust a command signal, an estimation oran estimation error of at least one of a hydrogen fuel flow rate 70, ananode leak rate 72 and an anode exhaust valve flow rate 74, as well asany other parameter of the fuel cell system 20 which depends upon (ormay benefit from) A_(Eff_True) for its calculation or determination.

FIG. 3 shows a flowchart for a method 100 of controlling or operatingthe fuel cell system 20. It should be noted that multiple embodiments ofthe method 100 are disclosed herein, and that some of these embodimentsmay not utilize all of the steps shown in FIG. 3 .

According to one embodiment, a method 100 is provided for controlling afuel cell system 20 having a hydrogen fuel injector/ejector 40 and acontrol system 60. In this embodiment, the method 100 includes: at block120, determining a hydrogen fuel consumption rate {dot over(n)}_(TrsntConsum) associated with a selected power level at steadystate; at block 130, obtaining a modeled hydrogen fuel flow rate {dotover (n)}_(injSp_Model) associated with the selected power level and theinjector/ejector 40; at block 210, estimating a true effective flow areaA_(Eff_True) of the injector/ejector, whereinA_(Eff_True)=A_(Eff_Model)·({dot over (n)}_(TrsntConsum)/{dot over(n)}_(injSp_Model)) (i.e., Eqn. 9), and where A_(Eff_Model) is a modeledeffective flow area associated with the injector/ejector 40; and, atblock 220, using the effective flow area A_(Eff_True) to calculate oradjust a command signal, an estimation or an estimation error of atleast one of a hydrogen fuel flow rate 70, an anode leak rate 72 and ananode exhaust valve flow rate 74.

At the selected power level at steady state, the anode pressure may bemaintained at a constant pressure. (For example, the anode pressure maybe the pressure measured by the pressure sensor 54 in the anode inputline 30, or a pressure measured inside the anode 24 itself.) The modeledhydrogen fuel flow rate {dot over (n)}_(injSp_Model) that is obtained atblock 130 may be obtained from a first look-up table 68 associated withthe control system 60, or it may be calculated by the control system 60(e.g., by the control software 64). Similarly, the modeled effectiveflow area A_(Eff_Model) may also be obtained at block 130 from a secondlook-up table 69 associated with the control system 60, or it may becalculated by the control system 60 (e.g., by the control software 64).(Note that this second look-up table 69 may be the same as the firstlook-up table 68, or it may be a different look-up table from the firstlook-up table 68.) The method 100 may further include, at block 110,operating the fuel cell system 20 at the selected power level and atsteady state, in order to determine the hydrogen fuel consumption rate{dot over (n)}_(TrsntConsum) associated with the selected power level atsteady state.

The fuel cell system 100 may include a PIA controller 56 operativelyassociated with the injector/ejector 40. (Note that the PIA controller56 may be used directly to control and/or monitor the hydrogen gas flowrate through the injector/ejector 40, and it may also be used indirectlyfor anode exhaust valve flow rate estimation and for slowly adapting theinjector effective flow area A_(Eff_True), as described herein.)Additionally, the true effective flow area A_(Eff_True) may be estimatedusing the equation A_(Eff_True)=A_(geo)·Coeff_(DC)·(1+a^(new)) (i.e.,Eqn. 14), where a^(new)=F_(x)·{dot over (n)}_(TrsntConsum)/({dot over(n)}_(TrsntConsum)+{dot over (n)}_(Leak_Model))−1 (i.e., Eqn. 19) andwhere F_(x)≈1+I_(A)·∫e dt+p_(A)·e+a^(old) (i.e., Eqn. 11). That is, Eqn.14, along with Eqns. 19 and 11, may be used instead of Eqn. 9 toestimate the true effective injector/ejector flow area A_(Eff_True). Inthe foregoing equations, A_(geo) is an orifice area of theinjector/ejector 40 that is determinable at a calibration event,Coeff_(DC) is an orifice discharge coefficient of the injector/ejector40 that is determinable at the calibration event, a^(new) is an updatedadaption term, F_(x) is an injector/ejector flow adjustment factoroutput by or derivable from the PIA controller 56, {dot over(n)}_(Leak_Model) is an anode leak rate calculated by the mass-balanceequation {dot over (n)}_(Leak_Model)={dot over (n)}_(injSp_Model)−{dotover (n)}_(TrsntConsum) (i.e., Eqn. 1), I_(A) is an integral gain of thePIA controller 56, p_(A) is a proportional gain of the PIA controller56, e is an error of the PIA controller 56 modeled by {dot over(n)}_(injSp_Model)−{dot over (n)}_(TrsntConsum), ∫e dt is a timeintegral of the error e, and a^(old) is a previous adaption term storedin a non-volatile memory 66 associated with the control system 60.

The method 100 may further include, at block 170, storing the updatedadaption term a^(new) in the non-volatile memory 66, or it may include,at block 180, replacing the previous adaption term a^(old) stored in thenon-volatile memory 66 with the updated adaption term a^(new).Additionally, the anode leak rate {dot over (n)}_(Leak_Model) may be anaveraged anode leak rate stored in the non-volatile memory 66.

According to another embodiment, a method 100 of operating a fuel cellsystem 20 having a hydrogen fuel injector/ejector 40, an anode 24, a PIAcontroller 56 operatively associated with the injector/ejector 40, acontrol system 60 and a non-volatile memory 66 associated with thecontrol system 60 includes the following steps. At block 110, the fuelcell system 20 is operated at a selected power level for a predeterminedtime. At block 120, a hydrogen fuel consumption rate {dot over(n)}_(TrsntConsum) associated with the power level is determined. Atblock 130, a modeled hydrogen fuel flow rate {dot over(n)}_(injSp_Model) associated with the selected power level and theinjector/ejector 40 is obtained. At block 140, an anode leak rate {dotover (n)}_(Leak_Model) of the anode 24 is found, where {dot over(n)}_(Leak_Model)={dot over (n)}_(injSp_Model)−{dot over(n)}_(TrsntConsum). The modeled anode leak rate {dot over(n)}_(Leak_Model) may or may not be averaged values. And at block 160,an adaption term a^(new) is calculated, where a^(new)=(1+I_(A)·∫edt+p_(A)·e+a^(old))·{dot over (n)}_(TrsntConsum)/({dot over(n)}_(TrsntConsum)+{dot over (n)}_(Leak_Model))−1, in which I_(A) is anintegral gain of the PIA controller 56, p_(A) is a proportional gain ofthe PIA controller 56, e is an error of the PIA controller 56, ∫e dt isa time integral of the error e, and a^(old) is a previously calculatedor provided adaption term stored in the non-volatile memory 66.

The method 100 may further include, at block 170, storing the calculatedadaption term a^(new) in the non-volatile memory 66. Alternatively, themethod 100 may include, at block 180, comparing the calculated adaptionterm a^(new) with the previously calculated or provided adaption terma^(old), and, at block 190, replacing the previously calculated orprovided adaption term a^(old) in the non-volatile memory 66 with thecalculated adaption term a^(new) if the difference between the adaptionterms a^(old) and a^(new) is greater than a predetermined value. Themethod 100 may further include, at block 150, storing the anode leakrate {dot over (n)}Leak_Model in the non-volatile memory 66.

This embodiment above may further include, at block 200, repeating theoperating, determining, obtaining, finding and calculating steps (i.e.,blocks 110, 120, 130, 140 and 160) for a plurality of times fordifferent power levels from the initial power level (e.g., until aminimum number of repetitions/power levels have been completed). In eachrepeat of the calculating step at block 160, the respective calculatedadaption term a^(new) for that iteration may be stored in non-volatilememory 66 as either (i) a replacement for a previously calculatedadaption term or (ii) an average and/or an accumulation of some or allof the previous adaption terms. The method 100 may also include, atblock 210, estimating a true effective flow area A_(Eff_True) of theinjector/ejector, using either A_(Eff_True)=A_(Eff_Model)·({dot over(n)}_(TrsntConsum)/{dot over (n)}_(injSp_Model)) (i.e., Eqn. 9) orA_(Eff_True)=A_(geo)·Coeff_(DC)·(1+a^(new)) (i.e., Eqn. 14), in whichA_(Eff_Model) is a modeled effective flow area associated with theinjector/ejector 40, A_(geo) is an orifice area of the injector/ejector40 and Coeff_(DC) is an orifice discharge coefficient of theinjector/ejector 40, and, at block 220, using the effective flow areaA_(Eff_True) to calculate or adjust a command signal, an estimation oran estimation error of at least one of the hydrogen fuel flow rate 70,the anode leak rate 72 and the anode exhaust valve flow rate 74. At eachselected power level operating at steady state, the anode pressure maybe maintained at a constant pressure. Each of the modeled hydrogen fuelflow rate {dot over (n)}_(injSp_Model) and the modeled effective flowarea A_(Eff_Model) may be obtained from a look-up table 68, 69associated with the control system 60, or they may be calculated by thecontrol system 60.

According to yet another embodiment, a method 100 of operating a fuelcell system 20 having a hydrogen fuel injector/ejector 40, an anode 24,a PIA controller 56 operatively associated with the injector/ejector 40,a control system 60 and a non-volatile memory 66 associated with thecontrol system 60, includes: at block 110, operating the fuel cellsystem 20 at a selected power level for a predetermined time; at block120, determining a hydrogen fuel consumption rate {dot over(n)}_(TrsntConsum) associated with the power level; at block 130,obtaining a modeled hydrogen fuel flow rate {dot over (n)}_(injSp_Model)associated with the selected power level and the injector/ejector 40; atblock 140, finding an anode leak rate {dot over (n)}_(Leak_Model) of theanode 24, where {dot over (n)}_(Leak_Model)={dot over(n)}_(injSp_Model)−{dot over (n)}_(TrsntConsum); at block 160,calculating an adaption term a^(new), where a^(new)=(1+I_(A)·∫edt+p_(A)·e+a^(old))·{dot over (n)}_(TrsntConsum)/({dot over(n)}_(TrsntConsum)+{dot over (n)}_(Leak_Model))−1, in which I_(A) is anintegral gain of the PIA controller, p_(A) is a proportional gain of thePIA controller, e is an error of the PIA controller, ∫e dt is a timeintegral of the error e, and a^(old) is a previously calculated orprovided adaption term stored in the non-volatile memory; at block 180,comparing the calculated adaption term a^(new) with the previouslycalculated or provided adaption term a^(old), at block 190, replacingthe previously calculated or provided adaption term a^(old) in thenon-volatile memory 66 with the calculated adaption term a^(new) if thedifference between the adaption terms a^(old) and a^(new) is greaterthan a predetermined value; at block 200, repeating the operating,determining, obtaining, finding, calculating, comparing and replacingsteps (i.e., blocks 110-140, 160, 180 and 190) for a plurality of timesfor power levels that are different from the initial power level; atblock 210, estimating a true effective flow area A_(Eff_True) of theinjector/ejector 40, using either Eqn. 9 (i.e.,A_(Eff_True)=A_(Eff_Model)·({dot over (n)}_(TrsntConsum)/{dot over(n)}_(injSp_Model))) or Eqn. 14 (i.e.,A_(Eff_True)=A_(geo)·Coeff_(DC)·(1+a^(new))), where A_(Eff_Model) is amodeled effective flow area associated with the injector/ejector 40,A_(geo) is an orifice area of the injector/ejector 40 and Coeff_(DC) isan orifice discharge coefficient of the injector/ejector 40; and, atblock 220, using the effective flow area A_(Eff_True) to calculate oradjust a command signal, an estimation or an estimation error of atleast one of the hydrogen fuel flow rate 70, the anode leak rate 72 andthe anode exhaust valve flow rate 74.

The above description is intended to be illustrative, and notrestrictive. While the dimensions and types of materials describedherein are intended to be illustrative, they are by no means limitingand are exemplary embodiments. In the following claims, use of the terms“first”, “second”, “top”, “bottom”, etc. are used merely as labels, andare not intended to impose numerical or positional requirements on theirobjects. As used herein, an element or step recited in the singular andpreceded by the word “a” or “an” should be understood as not excludingplural of such elements or steps, unless such exclusion is explicitlystated. Additionally, the phrase “at least one of A and B” and thephrase “A and/or B” should each be understood to mean “only A, only B,or both A and B”. Moreover, unless explicitly stated to the contrary,embodiments “comprising” or “having” an element or a plurality ofelements having a particular property may include additional suchelements not having that property.

The flowcharts and block diagrams in the drawings illustrate thearchitecture, functionality and/or operation of possible implementationsof systems, methods and computer program products according to variousembodiments of the present disclosure. In this regard, each block in theflowchart or block diagrams may represent a module, segment or portionof code, which includes one or more executable instructions forimplementing the specified logical function(s). It will also be notedthat each block of the block diagrams and/or flowchart illustrations,and combinations of blocks in the block diagrams and/or flowchartillustrations, may be implemented by hardware-based systems that performthe specified functions or acts, or combinations of hardware andcomputer instructions. These computer program instructions may also bestored in a computer-readable medium that can direct a controller orother programmable data processing apparatus to function in a particularmanner, such that the instructions stored in the computer-readablemedium produce an article of manufacture including instructions toimplement the functions and/or actions specified in the flowcharts andblock diagrams.

This written description uses examples, including the best mode, toenable those skilled in the art to make and use devices, systems andcompositions of matter, and to perform methods, according to thisdisclosure. It is the following claims, including equivalents, whichdefine the scope of the present disclosure.

1. A method for controlling a fuel cell system having a hydrogen fuelinjector/ejector and a control system, comprising: determining ahydrogen fuel consumption rate {dot over (n)}_(TrsntConsum) associatedwith a selected power level at steady state; obtaining a modeledhydrogen fuel flow rate {dot over (n)}_(injSp_Model) associated with theselected power level and the injector/ejector; estimating a trueeffective flow area A_(Eff_True) of the injector/ejector, whereinA_(Eff_True)=A_(Eff_Model)·({dot over (n)}_(TrsntConsum)/{dot over(n)}_(injSp_Model)) and A_(Eff_Model) is a modeled effective flow areaassociated with the injector/ejector; and using the effective flow areaA_(Eff_True) to calculate or adjust a command signal, an estimation oran estimation error of at least one of a hydrogen fuel flow rate, ananode leak rate and an anode exhaust valve flow rate.
 2. The method ofclaim 1, wherein at the selected power level at steady state, an anodepressure is maintained at a constant pressure.
 3. The method of claim 1,wherein the modeled hydrogen fuel flow rate {dot over (n)}_(injSp_Model)is obtained from a first look-up table associated with the controlsystem or is calculated by the control system.
 4. The method of claim 1,wherein the modeled effective flow area A_(Eff_Model) obtained from asecond look-up table associated with the control system or is calculatedby the control system.
 5. The method of claim 1, further comprising:operating the fuel cell system at the selected power level and at steadystate, in order to determine the hydrogen fuel consumption rate {dotover (n)}_(TrsntConsum) associated with the selected power level atsteady state.
 6. The method of claim 1, wherein the fuel cell systemincludes a proportional-integral-adaptive (PIA) controller operativelyassociated with the injector/ejector.
 7. The method of claim 6, whereinthe true effective flow area A_(Eff_True) is estimated usingA_(Eff_True)=A_(geo)·Coeff_(DC)·(1+a^(new)), where a^(new)=F_(x)·{dotover (n)}_(TrsntConsum)/{dot over (n)}_(TrsntConsum)+_(Leak_Model))−1and F_(x)≈1+I_(A)·∫e dt+p_(A)·e+a^(old), in which: A_(geo) is an orificearea of the injector/ejector that is determinable at a calibrationevent; Coeff_(DC) is an orifice discharge coefficient of theinjector/ejector that is determinable at the calibration event; a^(new)is an updated adaption term; F_(x) is an injector/ejector flowadjustment factor output from the PIA controller; {dot over(n)}_(Leak_Model) is an anode leak rate calculated by {dot over(n)}_(Leak_Model)={dot over (n)}_(injSp_Model)−{dot over(n)}_(TrsntConsum); I_(A) is an integral gain of the PIA controller;p_(A) is a proportional gain of the PIA controller; e is an error of thePIA controller; ∫e dt is a time integral of the error e; and a^(old) isa previous adaption term stored in a non-volatile memory associated withthe control system.
 8. The method of claim 7, further comprising:storing the updated adaption term a^(new) in the non-volatile memory. 9.The method of claim 7, further comprising: replacing the previousadaption term a^(old) stored in the non-volatile memory with the updatedadaption term a^(new).
 10. The method of claim 7, wherein {dot over(n)}_(Leak_Model) is an averaged anode leak rate stored in thenon-volatile memory.
 11. A method of operating a fuel cell system havinga hydrogen fuel injector/ejector, an anode, aproportional-integral-adaptive (PIA) controller operatively associatedwith the injector/ejector, a control system and a non-volatile memoryassociated with the control system, comprising: operating the fuel cellsystem at a power level for a predetermined time; determining a hydrogenfuel consumption rate {dot over (n)}_(TrsntConsum) associated with thepower level; obtaining a modeled hydrogen fuel flow rate {dot over(n)}_(injSp_Model) associated with the selected power level and theinjector/ejector; finding an anode leak rate {dot over (n)}_(Leak_Model)of the anode, where {dot over (n)}_(Leak_Model)={dot over(n)}_(injSp_Model)−{dot over (n)}_(TrsntConsum); and calculating anadaption term a^(new), where a^(new)=(1+I_(A)·∫edt+p_(A)·e+a^(old))·{dot over (n)}_(TrsntConsum)/({dot over(n)}_(TrsntConsum)+{dot over (n)}_(Leak_Model))−1, in which I_(A) is anintegral gain of the PIA controller, p_(A) is a proportional gain of thePIA controller, e is an error of the PIA controller, ∫e dt is a timeintegral of the error e, and a^(old) is a previously calculated orprovided adaption term stored in the non-volatile memory.
 12. The methodof claim 11, further comprising: storing the calculated adaption terma^(new) in the non-volatile memory.
 13. The method of claim 11, furthercomprising: comparing the calculated adaption term a^(new) with thepreviously calculated or provided adaption term a^(old); and replacingthe previously calculated or provided adaption term a^(old) in thenon-volatile memory with the calculated adaption term a^(new) if thedifference between the adaption terms a^(old) and a^(new) is greaterthan a predetermined value.
 14. The method of claim 11, furthercomprising: storing the anode leak rate {dot over (n)}_(Leak_Model) inthe non-volatile memory.
 15. The method of claim 11, further comprising:repeating the operating, determining, obtaining, finding and calculatingsteps for a plurality of times for different power levels from theinitial power level.
 16. The method of claim 15, wherein in each repeatof the calculating step, the respective calculated adaption term a^(new)is stored in the non-volatile memory as either (i) a replacement for apreviously calculated adaption term or (ii) an average and/oraccumulation of some or all of the previous adaption terms.
 17. Themethod of claim 11, further comprising: estimating a true effective flowarea A_(Eff_True) of the injector/ejector, using one ofA_(Eff_True)=A_(Eff_Model)·({dot over (n)}_(TrsntConsum)/{dot over(n)}_(injSp_Model)) and A_(Eff_True)=A_(geo)·Coeff_(DC)·(1+a^(new)), inwhich A_(Eff_Model) is a modeled effective flow area associated with theinjector/ejector, A_(geo) is an orifice area of the injector/ejector andCoeff_(DC) is an orifice discharge coefficient of the injector/ejector;and using the effective flow area A_(Eff_True) to calculate or adjust acommand signal, an estimation or an estimation error of at least one ofa hydrogen fuel flow rate, an anode leak rate and the anode exhaustvalve flow rate.
 18. The method of claim 11, wherein at the selectedpower level at steady state, an anode pressure is maintained at aconstant pressure.
 19. The method of claim 11, wherein each of themodeled hydrogen fuel flow rate {dot over (n)}_(injSp_Model) and themodeled effective flow area A_(Eff_Model) is obtained from a look-uptable associated with the control system or is calculated by the controlsystem.
 20. A method of operating a fuel cell system having a hydrogenfuel injector/ejector, an anode, a proportional-integral-adaptive (PIA)controller operatively associated with the injector/ejector, a controlsystem and a non-volatile memory associated with the control system,comprising: operating the fuel cell system at a power level for apredetermined time; determining a hydrogen fuel consumption rate {dotover (n)}_(TrsntConsum) associated with the power level; obtaining amodeled hydrogen fuel flow rate {dot over (n)}_(injSp_Model) associatedwith the selected power level and the injector/ejector; finding an anodeleak rate {dot over (n)}_(Leak_Model) of the anode, where {dot over(n)}_(Leak_Model)={dot over (n)}_(injSp_Model)−{dot over(n)}_(TrsntConsum); calculating an adaption term a^(new), wherea^(new)=(1+I_(A)·∫e dt+p_(A)·e+a^(old))·{dot over(n)}_(TrsntConsum)/({dot over (n)}_(TrsntConsum)+{dot over(n)}_(Leak_Model))−1, in which I_(A) is an integral gain of the PIAcontroller, p_(A) is a proportional gain of the PIA controller, e is anerror of the PIA controller, ∫e dt is a time integral of the error e,and a^(old) is a previously calculated or provided adaption term storedin the non-volatile memory; comparing the calculated adaption terma^(new) with the previously calculated or provided adaption terma^(old); replacing the previously calculated or provided adaption terma^(old) in the non-volatile memory with the calculated adaption terma^(new) if the difference between the adaption terms a^(old) and a^(new)is greater than a predetermined value; repeating the operating,determining, obtaining, finding, calculating, comparing and replacingsteps for a plurality of times for different power levels from theinitial power level; estimating a true effective flow area A_(Eff_True)of the injector/ejector, using one of A_(Eff_True)=A_(Eff_Model)·({dotover (n)}_(TrsntConsum)/{dot over (n)}_(injSp_Model)) andA_(Eff_True)=A_(geo)·Coeff_(DC)·(1+a^(new)), in which A_(Eff_Model) is amodeled effective flow area associated with the injector/ejector,A_(geo) is an orifice area of the injector/ejector and Coeff_(DC) is anorifice discharge coefficient of the injector/ejector; and using theeffective flow area A_(Eff_True) to calculate or adjust a commandsignal, an estimation or an estimation error of at least one of ahydrogen fuel flow rate, an anode leak rate and the anode exhaust valveflow rate.